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One of the most influential algorithms in data mining, k-means, is broadly used in practical tasks for its simplicity, computational efficiency and effectiveness in high dimensional problems. However, k-means has two major drawbacks, which are the need to choose the number of clusters, k, and the sensibility to the initial prototypes' position. In this work, systematic, evolutionary and order heuristics used to suppress these drawbacks are compared. 27 variants of 4 algorithmic approaches are used to partition 324 synthetic data sets and the obtained results are compared.

Hierarchical density-based clustering is a powerful tool for exploratory data analysis, which can play an important role in the understanding and organization of datasets. However, its applicability to large datasets is limited because the computational complexity of hierarchical clustering methods has a quadratic lower bound in the number of objects to be clustered. MapReduce is a popular programming model to speed up data mining and machine learning algorithms operating on large, possibly distributed datasets. In the literature, there have been attempts to parallelize algorithms such as Single-Linkage, which in principle can also be extended to the broader scope of hierarchical density-based clustering, but hierarchical clustering algorithms are inherently difficult to parallelize with MapReduce. In this paper, we discuss why adapting previous approaches to parallelize Single-Linkage clustering using MapReduce leads to very inefficient solutions when one wants to compute density-based clustering hierarchies. Preliminarily, we discuss one such solution, which is based on an exact, yet very computationally demanding, random blocks parallelization scheme. To be able to efficiently apply hierarchical density-based clustering to large datasets using MapReduce, we then propose a different parallelization scheme that computes an approximate clustering hierarchy based on a much faster, recursive sampling approach. This approach is based on HDBSCAN*, the state-of-the-art hierarchical density-based clustering algorithm, combined with a data summarization technique called data bubbles. The proposed method is evaluated in terms of both runtime and quality of the approximation on a number of datasets, showing its effectiveness and scalability.